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Introduction to Early Universe Cosmology

Observational cosmology is in its "golden age" with a vast amount of recent data on the distribution of matter and light in the universe. This data can be used to probe theories of the very early universe. It is small amplitude cosmological fluctuations which encode the information about the very early universe and relate it to current data. Hence, a central topic in these lectures is the "theory of cosmological perturbations", the theory which describes the generation of inhomogeneities in the very early universe and their evolution until the current time. I will apply this theory to three classes of models of the very early universe. The first is "Inflationary Cosmology", the current paradigm for understanding the early evolution of the universe. I will review the successes of inflationary cosmology, but will also focus on some conceptual challenges which inflationary cosmology is facing, challenges which motivate the search for possible alternatives. I will introduce two alternative scenarios, the "Matter Bounce" model and "String Gas Cosmology", and I will discuss how cosmological fluctuations which can explain the current data are generated in those models.